Equilibrium long-ranged charge correlations at the surface of a conductor coupled to the electromagnetic radiation

TL;DR

This paper investigates how retardation effects influence surface charge correlations on a conductor coupled to electromagnetic radiation, revealing a universal classical form of the correlation prefactor across temperatures.

Contribution

It extends previous models by incorporating retardation effects using Rytov's fluctuational electrodynamics, showing a universal behavior of charge correlations.

Findings

Retardation effects cause quantum prefactors to match classical static forms.

Surface charge correlations decay as inverse cube of distance.

Universal behavior observed at all temperatures.

Abstract

This study is related to the fluctuation theory of electromagnetic fields, charges and currents. The three-dimensional system under consideration is a semi-infinite conductor, modeled by the jellium, in vacuum. In previous theoretical studies it was found that the correlation functions of the surface charge density on the conductor decay as the inverse cube of the distance at asymptotically large distances. The prefactor to this asymptotic decay was obtained in the classical limit and in the quantum case without retardation effects. To describe the retarded regime, we study a more general problem of the semi-infinite jellium in thermal equilibrium with the radiated electromagnetic field. By using Rytov's fluctuational electrodynamics we show that, for both static and time-dependent surface charge correlation functions, the inclusion of retardation effects causes the quantum prefactor to take its universal static classical form, for any temperature.